An understanding of the extra information contained in the reduced densities allow us to examine the mechanics of this DMRG algorithm and study the generalization error of the resulting model.Expand

Given a differential Batalin–Vilkovisky algebra (V, Q, Δ.) the associated odd differential graded Lie algebra (V, Q, + Δ, [,].) is always smooth formal. The quantum differential graded Lie algebra… Expand

This is the first of two papers that introduce a deformation theoretic framework to explain and broaden a link between homotopy algebra and probability theory. In this paper, cumulants are proved to… Expand

We develop the deformation theory of A_\infty algebras together with \infty inner products and identify a differential graded Lie algebra that controls the theory. This generalizes the deformation… Expand

An efficient training algorithm for a subset of classically simulable quantum circuit models, presented as a sequence of exactly solvable effective models, is a modification of the density matrix renormalization group procedure adapted for learning a probability distribution.Expand

A novel generative algorithm is introduced giving trained u-MPS the ability to efficiently sample from a wide variety of conditional distributions, each one defined by a regular expression, which permits the generation of richly structured text in a manner that has no direct analogue in current generative models.Expand

We propose a statistical model for natural language that begins by considering language as a monoid, then representing it in complex matrices with a compatible translation invariant probability… Expand

We show that a square zero, degree one element in W(V), the Weyl algebra on a vector space V, is equivalent to providing V with the structure of an algebra over the properad Cobar(coFrob), the… Expand

A uniform matrix product state (u-MPS) model for probabilistic modeling of sequence data that has the ability to condition or marginalize sampling on characters at arbitrary locations within a sequence, with no need for approximate sampling methods.Expand